Isidoro Gitler, Carlos E. Valencia and Rafael H. Villarreal

Abstract: We study irreducible representations of Rees cones and characterize the max-flow min-cut property of clutters in terms of the normality of Rees algebras and the integrality of certain polyhedra. Then we present some applications to combinatorial optimization and commutative algebra. As a byproduct we obtain an effective method, based on the program Normaliz\/ [B], to determine whether a given clutter satisfies the max-flow min-cut property. Let $\cal C$ be a clutter and let $I$ be its edge ideal. We prove that $\cal C$ has the max-flow min-cut property if and only if $I$ is normally torsion free, that is, $I^i=I^{(i)}$ for all $i\geq 1$, where $I^{(i)}$ is the $i$-th symbolic power of $I$. [B] Bruns, W.; Koch, R.: Normaliz -- a program for computing normalizations of affine semigroups. 1998. Available via anonymous ftp from ftp.mathematik.Uni-Osnabrueck.DE/pub/osm/kommalg/software